The driver for this chip is in the Linux kernel module asix. This module will handle a lot of USB vendor/product combinations as of the version in Ubuntu's 3.5.0-18:
$ modinfo asix
filename: /lib/modules/3.5.0-18-generic/kernel/drivers/net/usb/asix.ko
license: GPL
description: ASIX AX8817X based USB 2.0 Ethernet Devices
version: 22-Dec-2011
author: David Hollis
srcversion: 0889AC645D9EA92D3DE4C5B
alias: usb:v0B95p7E2Bd*dc*dsc*dp*ic*isc*ip*
alias: usb:v0DB0pA877d*dc*dsc*dp*ic*isc*ip*
<snip>
alias: usb:v0846p1040d*dc*dsc*dp*ic*isc*ip*
alias: usb:v077Bp2226d*dc*dsc*dp*ic*isc*ip*
depends: usbnet
intree: Y
However, I find some (old) bug stating it won't work out of the box in Debian. And, more importantly, if you need this in a Live environment, make sure it is one with one of these packages installed into.